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lfunc_lfunctions • Show schema
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{'Lhash': '2383193820517000387120100354494', 'a10': [-2.3634767381757085, -4.093661793027492], 'a2': [-1.2340378417106002, -2.137416240305399], 'a3': [1.6229241192456665, 0.6050762788034895], 'a4': [-2.045698789547512, 3.5432542404784435], 'a5': [1.9152384621362188, 0.0], 'a6': [-0.7094499124358629, -4.215551394423963], 'a7': [-0.3247084524793541, 0.5624115373413057], 'a8': [5.1617275093303965, 0.0], 'a9': [2.2677653936586437, 1.9639857737071966], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.6229241192456665, -0.6050762788034895]]], [19, [[1.0, 0], [4.284383943965794, 0.8025298877226377]]]], 'bad_primes': [3, 19], 'central_character': '171.106', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '2170584204117601601854324785458', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.2340378417106002, 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'7.61268050746769297682594071628847', '9.083139576180760988120543481852566', '9.325887357725773294935539976768960', '10.30261371659872136522659335992907', '12.26855229063827268401150450303758', '13.51671888541406530862662996934706'], 'prelabel': '2-171-171.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.44059916770993335, 'root_number': '0.18553198426849288 + 0.9826382258051005*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.220299583855', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.88000843457016246218744997059', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.39297966952684168607043247205', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.03666164506989404516090252639', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '171.106', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/g/c/106/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-171-171.106-c1-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-171-171.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.22029958385496667, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.88000843457016246218744997059', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2383193820517000387120100354494', 'Lhash_array': ['2383193820517000387120100354494'], 'label': '2-171-171.106-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/g/c/106/1'}